Piezo-electric quartz crystal of elongated shape



Feb. 16, 1960 c. FRANX 2,925,502

PIEZO-ELECTRIC QUARTZ CRYSTAL OF ELONGATED SHAPE Filed Dec. 18, 1957 2 Sheets-Sheet 1 R T p l 1 I l I +36 28 20 I2 4 0-4 -|2 -20 2B OSCI L- LATOR INVENTOR CORNELIS FRANX AG T C. FRANX Feb. 16, 1960 PIEZO-ELECTRIC QUARTZ CRYSTAL OF ELONGATED SHAPE Filed Dec. l8, 1957 2 Sheets-Sheet 2 INVENTOR CORNELIS FRANX AGE United States Patent PIEZO-ELECTRIC QUARTZ CRYSTAL OF ELONGATED SHAPE Cornelis Franx, Eindhoven, Netherlands, assignor to North American Philips Company Inc., New York, N.Y., a corporation of Delaware Application December 18, 1957, Serial N 0. 703,655

' Claims priority, application Netherlands December 21, 1956 3 Claims. (Cl. 310-95) .This invention relates to piezo-electric quartz crystals of elongated shape which are capable of performing longitudinal oscillations, more particularly quartz crystals of X-cut.

Such crystals may be used'as frequency stabilisers or filters in the frequency range of from 50-200 kc./s. Especially in the last-mentioned application, there is frequently interference from spurious resonance in this range, which results from the fact that the crystal can also perform flexural oscillations. With quartzcrystals of X-cut, the spurious resonance may be suppressed by a determined choice of the angle made by the long side of the crystal and the Y-axis, since spurious resonance does not occur if this angle is about 18.5. However, the temperature coefficient of the crystal is unduly high for this value. The limitation to the value of 18.5 is also disadvantageous in other respects, since some freedom in the choice of said angle is desirable to permit the further parameters of the crystal, such as for example the inductance, to be chosen according to requirements.

An vobect of the invention is to provide steps by which the spurious resonance is suppressed at all orientations of the long side of the crystal including, for the X-cut, values of said angle which difler from 18.5. According to the invention, this is achieved due to the largest surface of the crystal having the shape of a parallelogram having angles differing from 90 to an extent such that the crystal is substantially free of the spurious resonance at which the crystal performs flexural vibrations of an even order. In order that the invention may be more readily carried into effect, it will now be described more fully, by way of example, with reference to the accompanying drawing, in which:

Fig. 1 illustrates the difficulties which occur with crystals of known type;

Figs. 2 and 3 serve to explain these difliculties and the principle underlying the invention, Fig. 2 showing an example of a crystal according to the invention;

Fig. 4 shows a measuring circuit of known type and Fig. 5 represents a second example of a crystal according to the invention.

Itis known (see .Cady, Piezo-Electricity l946,'pages 104406) that a longitudinally oscillating piezo-crystal, for example a quartz crystal of X-cut, that is a crystal having its largest surface at right angles to the X-axis, does not usually perform purely longitudinal oscillations and that the oscillations (see Fig. 1) have a transverse component T in addition to the longitudinal component L, so that the resulting deviation R of the oscillating crystal parts makes a certain angle with the direction of length of the crystal. The transverse component T has the effect, that the flexural oscillation of the crystal may be excited in accordance with the pattern shown in dotted line (second order flexural oscillation), the resonance frequency of which is adjacent that of the main oscillation and may be very troublesome. It may be shown both empirically and by calculation that the transverse comice ponent is nil only with an orientation of the long side of the X-crystal of 18.5 with respect to the Y-axis. In the annotation used by Cady this angle was indicated'as +18.5.)

In general, it may be assumed that in an oscillating anisotropic medium the direction of propagation of the oscillations, which direction is at right angles tothe wave front F and hence-coincident with the perpendicular N to this wave-front, makes a certain angle (p with the deviation (amplitude) R. For a quartz crystal of X-cut' (see Fig. 2) this angle (p is dependent upon the angle 0 between the perpendicular N and the Y-axis (see Fig. 2)

and is plotted in Fig. 3 as a function of the angle (H 0) between the deviationR and the Y-axis'. This graph shows that =0 at 0+=approximately -18". For a rectangular crystal, the direction of length of which has this orientation, the oscillation is purely longitudinal and R and N are both parallel to the direction of length of the crystal.

If the direction of length of the crystal has a different orientation, for example the value +5", which is adl vantageous in view of the temperature coeflicient, the

deviation R for a rectangular crystal, since the perpendicular N and the deviation R are not coincident, is no longer parallel to the direction of length (the long side) of the crystal but makes a certain angle with the long side, so that a transverse oscillation component occurs.

According to the invention, this may be avoided by choosing the angle between the two sides of the crystal face to be different from 90, the crystal thus having the form of a parallelogram with angles differing from 90. If the -previously chosen-orientation of the long side of the crystal is +5, the desired value of the angle 0+ also=5, because evidently at this same value the deviation R actually lies in the direction of length of the crystal. This obtained'if the (smallest) angle be tween the sides of the parallelogram-like crystal (shown in dotted line) is 90 amounting, in the case under consideration, to 90l7=about 73 (see Fig. 3). As a matter of fact, the short side must be at right angles to N.

The angle 90- may best be determined empirically, it being possible for quartz crystals of X-cut to derive, if desired, a first approximation for said angle from the curve shown in Fig. 3. For the sake of simplicity, the most important portion of the .curve between 0+ =2 and 0+ =+l4 may be considered as straight. The curve may then be approximately represented by-the equation.

=14.4+0.74 (0+ga) degrees 1 spurious oscillation is suppressed as far as possible. By

the step according to the invention, it is possible for the activity of the spurious oscillation to be reduced by factor or upwards. However, such considerable suppression may require a veryaccurate and expensive manufacture, so that for reasons of cost it may be preferable to be satisfied with a much less thorough suppression, for example by a factor from 2 to 3. The angle o may in this case considerably differ (for example :10?) from the value found from the equation. The extent to which the spurious oscillation is suppressed may be determined by measuring the series resistance R of the crystal.

The impedance of a piezo-electric crystal in the circuits of the main resonance and of the additional (spurious) resonance respectively may be represented with good approximation by the series-combination of inductance L and L' series-resistors R and R' and capacitors C and C' respectively, the assembly shunted by parallel capacitors C, and C respectively. For determining the loss resistance R' at the additional resonance, use may be made of the measuring circuit shown in Fig. 4.

In this circuit, the crystal 1 to be measured constitutes one branchof a measuringbridge, the other branches It isknown to utilize this fact for slightly suppressing the additional oscillation, the disadvantage of a likewise attenuated main oscillation also being taken into consideration. With the crystal according to the invention, since being constituted bythe two halves of the secondary 5 the additional oscillation is already materially suppressed, winding-Of a symmetric transformer 3 and by a variable this disadvantage may be avoided by the use of a comparacapacitor 5. The transformer 3 is fed, at its primary side, tively high 'vacuum- T e Vacuum y "advantageously byanoscillator 7pand1the secondary. voltage (2V ocbe more than 50% (less than 380 mms. of mercury cursacross one diagonal of the bridge. The other diagpressure), for example 90%. onal is constituted by a reference resistor 9. The volt- 10 The invention is also applicable to longitudinally oscilage- (V which occurs across the resistor is supplied lating crystals of a cut in which, incontradistinction to through a filter 11, which interrupts the harmonics presthe X-cut the perpendicular to the largest surface of the out in the output voltage of oscillator 7, to a sensitive crystal is not parallel to the X-axis, such as crystals of voltmeter 13., e MT-cut. These crystals may be imagined to he obtained [The oscillator 7 is adjusted toa frequency slightly from an X-cut crystal by. tiltingit with respect to the differingfrom the additional resonance, the bridge being reference axes about one of the long sides of the crystal brought into equilibrium (V minimum) by means of plate. In order to satisfy the conditions for the occurcapacitor 5.. Subsequently, the .oscillator frequency is rence of a purely longitudinal oscillation, it is desirable readjusted till V -is maximum. During this adjustment forthe'se kinds of crystals not only that the angles ofthe V ;isal so measured. largest surface "of the crystal differ from 90, butalso If the value R of resistance 9 is so chosen that that the end surfaces of the crystal make angles with the 1 largest surface whichdiifer from 90. Fig. 5 shows 'R;, R and R an example of 'such 'an MT-crystal. Itis derived from i I a'r'ectang'ular MT-crystal (shown in dotted lines) which (w= gu1er frequency, c=value of cap-acitorfS), then has an orientation (Y, Z) of 8 "with respect to the applies Y-(and Z-')'axis and a tilting angle of 34. with respect to V the Y;Z. plane. The (acute). angle between adjacent k= 7 sides of the large face of the crystal according to the in- U A 2 V vention is about 72 and theacute angle between the am measured i a 0- oyscylllato'r 30 largest and'the Smallest face of the crystal (which is y method of t sllbstltutimlby a known resistor equal tojthe angle between the'perpendiculars N and N (*see, for example,,the' articleby Gerber, A'Review of to these f is 79 Methods for Measuring the Constants of Piezo-Electnc What is claimed i i V D SJFQ -I 9 11 25 1106) V l. A piezo-electric crystal having a length-Wise di- The relation 35 mension exceeding dimensions in directions perpendicular R thereto and being adapted to vibrate along said lengthi 1?; Wise dimension, said crystal having at least one surface a v whose dimensionsexceed those of another surface and is a measure of the suppressionof the additional resonwhich extends in the direction of said lengthwise ance. The table followmg herelnafter shows the results 40 mension, and the edges of which define a parallelogram, 9 S fi l l On o rectangular 9 Y and P adjoining edges of said parallelogram defining angles pa g a r crystals (i= q y; T'= d which difier from 90 by an amount at'which the crystal tidnal q y; l=length of longest side mm; is substantially free of the spurious resonance at which b=width; d=thickness of the crystal). the crystal performs fiexural oscillations of an even order.

RECTANGULAR oRYsTA'Ls j 1' R1. R's R 's 'z b a e+ +90 PARALLEL'oGRAM-LIKE CRYSTALS 107.74 75 t 260 1.9M 7.3.10 26.1 3.71 0.8 5 am. 71 107.76 74.9 a 150 12M 8.10 Y 26.1 .3. 71 0.8 5 abt. 71

. T F $h t the relation 2. piezo-electric crystal having a length-wise dimension exceeding dimensions'in directions perpendicu- -klar thereto and being adapted to vibrate along said length- I V r Wise d1merision, said crystal having at least one surface for crystals" according to the invention may be a factor Whose normal thereto forms an angle other than 90 with several hundreds larger than for crystals of known type. I the 'X-axisand whose dimensions exceed those of another This appl es,- of course also for orientation angles difierent l f cei Which H n th direction of Said length from For-example, in an 80 kc. crystal (1 :56 kc.) Wise dimension, and the edges'of which define a parallelowith an orientation of about 2 an 7 gram, adjoining edges of said parallelogram defining R9: angles which differ from 90 by an amount'at which the T crystal 1s; substantially free. of the spurious resonance at k Whlch the crystal performs fl'exural oscillations of an relation of about 2.6.10 was measured. I Y .The crystal may be housed in a hermetic envelope which is partly exhausted. The gas contained 'in the envelope has .a damping. effect upon the additional oscillation and, to a lesser extent, upon the mainoscillation.

even order, said surface forming with adjoining surfaces of the crystal angles which differ from 3. A piezo-electric crystal having a length-wise dimension exceeding dimensions 1 in directions perpendicular thereto and being adapted to -vibrate along said lengthwise dimension, said crystal having at least one surface whose normal is parallel to the X-axis of the crystals and Whose dimensions exceed those of another surface and which extends in the direction of said lengthwise dimension, and the edges of which define a parallelogram, adjoining edges of said parallelogram defining angles which differ from 90 by an amount at which the crystal is substantially free of the spurious resonance at which the crystal performs fiexural oscillations of an even order.

6 References Cited in the file of this patent UNITED STATES PATENTS Mason Jan. 11, 1949 OTHER REFERENCES Cady: Piezoelectricity, McGraw-Hill Book Co. Inc., New York, New York, copyright 1956, pages 456-457. 

